Has spacetime some physical properties?

Question

"Spacetime isn't a physical object, it's a mathematical structure (manifold with metric) that tells us how to calculate the distance between objects, so matter can't slide over spacetime." (John Rennie, What is the difference between matter & spacetime?, https://physics.stackexchange.com/q/129315 .)

However, there exists solution [1] of Einstein's field equations describing a static spherically symmetric space-time without matter ($\varepsilon=0$) but with pressure ($p\ne 0$) which by definition is a volumetric stress. Well, the question is a stress of what? Furthermore, there exists the universal maximal tension [2] that gives rise to emergence of event horizon, i.e. to some kind of ripping open the spacetime. And last but not least, without matter there would be no spacetime [3] and vice versa, as Einstein said and Big Bang theory suggests. These all could be interpreted that spacetime posses some physical properties.

[1] https://physics.stackexchange.com/a/679431/281096, see equations (11)-(14),

[2] https://physics.stackexchange.com/a/707944/281096,

[3] https://physics.stackexchange.com/a/698092/281096

Answer 1

This is more a long comment than an answer, you can skip until the end if you want.

I am not a downvoter but I had a notification and regarding your comments, it appears to me that you are confusing two things:

1. Space-time is a mathematical framework, and we build our theories on it.

2. The consequences of general relativity, a theory of space-time, are observable and in a sense 'real'.

But the successes of our theories built on space-time (whether it is curved or not), say nothing about the realness of this mathematical concept. There is for example the block universe interpretation, which is a philosophical viewpoint of space-time saying that every instant of the universe exists, and the appearance of the flowing of time is but an illusion. What I mean here is that if there are different interpretations of space-time in general relativity, then the concept is unclear in common sense, even though mathematically speaking, it is perfectly defined.

Another possible interpretation is that space-time is an a posteriori concept. I mean by this the following:

• Each instant passes in 'reality' (with your definition of it) and when we pile them up, we can describe what happened with theories in the framework of space-time.

This is very different from saying 'space-time is real', and it fits nicely with the way physical theories are thought of: just mathematical entities that describe what is happening in experiments. Indeed an a posteriori vision of these theories built on space-time may give the illusion we can predict events time after time. But in fact, we just constructed for future (or hypothetical) events a four-volume that can be thought of as the mathematical version of a 'mini-block universe', and it happens that the events inside it match the flowing of time in our observations.

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All this to say:

Frame dragging, time dilation, and all predictions of theories based on space-time that were observed do not mean space-time is real, just that we have a theory that fits the data. That is to say, the Universe works the way it does, we describe it through mathematics, but it doesn't mean the mathematical concepts involved are 'real' or have a physical counterpart.

I will go a little further and say that these very questions you are asking are the sign of this very unrealness of space-time.

Answer 2

To answer the question as originally posed:

Matter tells spacetime how to bend (i.e., "curve"), and spacetime tells matter how to move (i.e., follow a geodesic). More matter creates more curvature, and more curvature causes more bending of the path of a chunk of matter traveling nearby.

Since matter is convertible to energy, energy concentrations will also bend spacetime. The volumetric stress you mention is experienced by spacetime itself and represents the energy content of distorted spacetime.

Answer 3

Is spacetime then really only a mathematical object?

This type of question is basically a game of twisting people’s words.

The analogy I like to use is that of a map and a territory. People who use maps to navigate a territory understand that there is a difference between the map and the territory. Sometimes they will talk about the map and sometimes they will talk about the territory and sometimes they will talk about both without really making the distinction clear.

Here, here the key statement was “Spacetime isn't a physical object” meaning it is not made out of matter. He further says “it's a mathematical structure” meaning it is part of the map. He did not claim your distorted “Is spacetime then really only a mathematical object” meaning it is only on the map with no relation to the territory. A compass rose is on a map, but that doesn’t mean that north is not in the territory.

Indeed, spacetime is mathematical. It is the part of the math that describes the geometry of the universe. Geometry is part of math and and geometry is part of reality. So just because it is indeed mathematical does not imply that it is not also physical. Spacetime is mathematical, but to the best of our knowledge it is part of the math of the actual universe.